Solve (s^3)^frac{1{3}}

$$( s ^ { 3 } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$s$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\sqrt[3]{s^{3}}$$

To raise a power to another power, multiply the exponents.

$$s^{3\times \frac{1}{3}}$$

Multiply 3 times \frac{1}{3}.

$$s$$

Differentiate w.r.t. s

$$1$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$\frac{1}{3}\left(s^{3}\right)^{\frac{1}{3}-1}\frac{\mathrm{d}}{\mathrm{d}s}(s^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{3}\left(s^{3}\right)^{-\frac{2}{3}}\times 3s^{3-1}$$

Simplify.

$$s^{2}\left(s^{3}\right)^{-\frac{2}{3}}$$